2. Annual Progress Seminar
Speaker: Hamidul Ahmed (Department of Mathematics, IIT Bombay)
Title: Complete Nevanlinna-Pick Dirichlet series kernel and multiplier variety
Time, Day and Date: 3:00 - 4:00 p.m., Monday, September 30
Venue: Ramanujan Hall, Department of Mathematics
Abstract: In this talk, we will concentrate on Dirichlet series kernels, which are also complete Nevanlinna Pick (CNP) kernels. We will start with a characterization of such kernels. It is known that every CNP space is isometrically isomorphic to the Drury-Arveson space restricted to its smallest multiplier-variety. Therefore, determining the smallest multiplier-variety is crucial in our context. McCarthy and Shalit have shown that if we take CNP Dirichlet series kernels corresponding to d natural numbers which are log independent, then the smallest multiplier-variety is the full ball, and thus the RKHS corresponding to such Dirichlet series kernels are isometrically isomorphic to the Drury-Arveson space. In this talk, we will completely determine smallest multiplier-varieties for any CNP Dirichlet series kernels.